Brain Dump

Rectangular Hyperbola

Tags
math

Is a hyperbola with vertical asymptotes. For a parabola \( \frac{\,dy}{\,dx} \) is always \( - \frac{1}{t^2} \).

\begin{figure}
  \centering
  \begin{tikzpicture}
    % preamble \usepackage{amsmath}
    %\draw[gray!50, very thin,->] (-4,0) -- (4,-0); % x-axis
    %\draw[gray!50, very thin,->] (0,-3) -- (0,3);  % y-axis
    %\draw[gray!50, very thin] (-2,-1.5) rectangle (2,1.5);
    \draw[black, ultra thick, ->] (0, -3) -- (0, 3) node[left]{$y$};
    \draw[black, ultra thick, ->] (-3.5, 0) -- (4, 0) node[below]{$x$};
    \draw[very thin, gray!30, step=1 cm](-3.9,-2.9) grid (3.9,3.9);

    \draw[domain=-1.3:1.3,smooth,variable=\t] plot ({2*cosh(\t)},{1.5*sinh(\t)});
    \draw[domain=-1.3:1.3,smooth,variable=\t] plot ({-2*cosh(\t)},{1.5*sinh(\t)});
    \draw [red!20, dashed, line width=0.5mm] (-4,-3) -- (4,3);
    \draw [red!20, dashed, line width=0.5mm] (4, -3) -- (-4,3);
  \end{tikzpicture}

  \caption{A rectangular hyperbola.}
\end{figure}